Factorization of 7,254+
 

The NFSNET Factoring group is pleased to announce the factorization of 7^254+1.

The linear algebra phase completed on Sunday April 10th at about 15:30 GMT.

The square root phase was started shortly afterwards. Each dependency required about 35 minutes on an Athlon XP 2000+ machine. The following factors were found on the 2nd dependency:

Original number had 178 digits:
709248894314890389794407514298791904291187459886465 \
560345452325830304907056818194681534554179221606885 \
277858349842944071910139694602168281008461470250300 \
9071296074419099802941233

Probable prime factor 1 has 69 digits:
206298375590160646565940288626398300890112694477191 \
593608184249768901

Probable prime factor 2 has 110 digits:
343797614637503647021667630776053249074476404018137 \
402521505530648614576887163343890661060504549666258 \
84817533

As mentioned in a previous posting, approximately 45.8 million relations were collected. Richard Wackerbarth performed singleton and duplicate removal on the data set reducing it to about 29.4M relations. Those relations were transferred to me for the post-processing steps.

Post-processing produced a matrix with 2710221 rows and 2711324 columns and a weight of 171991657. Thirteen of the rows for the smallest primes were excluded. The average prime weight is 63.46 and the average relation-set weight is 63.43.

Thanks to everyone who participated in this effort!

-Don Leclair

This is only an announcement, not a "question".